Current Electricity — Complete Formula

Electric Current

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Electric Current	[I = \dfrac{Q}{t}]	[I] = current, [Q] = charge, [t] = time	A	Rate of flow of charge ⭐
Drift Velocity Form	[I = nqAv_d]	[n] = number density, [q] = charge, [A] = area, [v_d] = drift velocity	A	Microscopic view ⭐

💡 Memory Hint:
Current = flow of charge per second

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Drift Velocity	[v_d = \dfrac{qE\tau}{m}]	[E] = electric field, [\tau] = relaxation time, [m] = mass	m/s	Very small value ⚠️
Mobility	[\mu = \dfrac{v_d}{E}]	[\mu] = mobility	m²/V·s	Important ⭐
Relation	[\mu = \dfrac{q\tau}{m}]	—	—	Derived relation

💡 Memory Hint:
Higher field → higher drift velocity

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Ohm’s Law	[V = IR]	[V] = voltage, [R] = resistance	V	Linear relation ⭐
Resistance	[R = \dfrac{V}{I}]	—	Ω	Opposition to current

💡 Memory Hint:
Voltage drives current through resistance

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Resistance	[R = \rho \dfrac{L}{A}]	[\rho] = resistivity, [L] = length, [A] = area	Ω	Depends on material ⭐
Resistivity	[\rho = \dfrac{RA}{L}]	—	Ω·m	Material property
Conductivity	[\sigma = \dfrac{1}{\rho}]	[\sigma] = conductivity	S/m	Inverse of resistivity

💡 Memory Hint:
Long wire ↑ R, thick wire ↓ R

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Resistance Change	[R = R_0(1 + \alpha \Delta T)]	[R_0] = initial resistance, [\alpha] = temp coefficient	Ω	Metals: R increases ⭐

💡 Memory Hint:
Temperature ↑ → resistance ↑ (metals)

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Series	[R_{eq} = R_1 + R_2 + \dots]	—	Ω	Current same ⭐
Parallel	[\dfrac{1}{R_{eq}} = \dfrac{1}{R_1} + \dfrac{1}{R_2}]	—	Ω	Voltage same ⭐

💡 Memory Hint:
Series ↑ resistance
Parallel ↓ resistance

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Power	[P = VI]	[P] = power	W	Basic relation ⭐
Alternate	[P = I^2 R]	—	W	Use when current known
Alternate	[P = \dfrac{V^2}{R}]	—	W	Use when voltage known

💡 Memory Hint:
Choose formula based on given values

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Energy	[E = Pt]	[E] = energy	J	Power × time ⭐
Joule Heating	[H = I^2 R t]	[H] = heat	J	Heating effect ⭐

💡 Memory Hint:
More current → more heating

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Current Law (KCL)	[\sum I_{in} = \sum I_{out}]	—	—	Junction rule ⭐
Voltage Law (KVL)	[\sum V = 0]	—	—	Loop rule ⭐

💡 Memory Hint:

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Balanced Condition	[\dfrac{R_1}{R_2} = \dfrac{R_3}{R_4}]	—	—	No current in bridge ⭐

💡 Memory Hint:
Balanced → no current in galvanometer

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Condition	[\dfrac{R}{S} = \dfrac{l}{100 – l}]	[l] = balancing length	—	Based on Wheatstone ⭐

💡 Memory Hint:
Bridge → ratio of resistances

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Potential Gradient	[k = \dfrac{V}{L}]	[k] = potential per unit length	V/m	Uniform wire ⭐
EMF Comparison	[\dfrac{E_1}{E_2} = \dfrac{l_1}{l_2}]	—	—	Very important ⭐

💡 Memory Hint:
No current drawn → accurate measurement

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